Backlash analysis of a new planetary gearing with internal gear ring

Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference.The kinematic calculation was conducted based on the analysis of structural composition and working principle.Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time.Then,main factors that affect the systematic backlash were introduced and the effects of manufacture error,misaligments and roller bearing parameters on the distribution of backlash were presented.The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed.The results show that the backlash is a little large,of which the backlash of bearing takes a greater part than two gearing stages.So we presented some practical methods to reduce the systematic backlash.

Parametric Analysis of the End Face Engagement Worm Gear

A novel specific type of worm drive, so-called end face engagement worm gear（EFEWD）, is originally presented to minimize or overcome the gear backlash. Different factors, including the three different types, contact curves, tooth profile, lubrication angle and the induced normal curvature are taken into account to investigate the meshing characteristics and create the profile of a novel specific type of worm drive through mathematical models and theoretical analysis. The tooth of the worm wheel is very specific with the sine-shaped tooth which is located at the alveolus of the worm and the tooth profile of a worm is generated by the meshing movement of the worm wheel with the sine-shaped tooth, but just the end face of the worm（with three different typical meshing types） is adapted to meshing, and therefore an extraordinary manufacturing methods is used to generate the profile of the end face engagement worm. The research results indicates that the bearing contacts of the generated conjugate hourglass worm gear set are in line contacts, with certain advantages of no-backlash, high precision and high operating efficiency over other gears and gear systems besides the end face engagement worm gear drive may improve bearing contact, reduce the level of transmission errors and lessen the sensitivity to errors of alignment. Also, the end face engagement worm can be easily made with superior meshing and lubrication performance compared with the conventional techniques. In particular, the meshing and lubrication performance of the end face engagement worm gear by using the end face to meshing can be increased over 10% and 7%, respectively. This investigate is expect to provide a new insight on the design of the future no-backlash worm drive for industry.

Bifurcation and chaos study on transverse-torsional coupled 2K-H planetary gear train with multiple clearances

A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.

Translational - torsional coupled model based nonlinear dynamic analysis of an NGW planetary gear train

This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational- torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains.

Effect of Tooth Profile Modification on Vibration of Power Split Gear Transmission System

Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.

A novel method to predict static transmission error for spur gear pair based on accuracy grade

This paper proposes a novel method to predict the spur gear pair’s static transmission error based on the accuracy grade,in which manufacturing errors(MEs),assembly errors(AEs),tooth deflections(TDs)and profile modifications(PMs)are considered.For the prediction,a discrete gear model for generating the error tooth profile based on the ISO accuracy grade is presented.Then,the gear model and a tooth deflection model for calculating the tooth compliance on gear meshing are coupled with the transmission error model to make the prediction by checking the interference status between gear and pinion.The prediction method is validated by comparison with the experimental results from the literature,and a set of cases are simulated to study the effects of MEs,AEs,TDs and PMs on the static transmission error.In addition,the time-varying backlash caused by both MEs and AEs,and the contact ratio under load conditions are also investigated.The results show that the novel method can effectively predict the range of the static transmission error under different accuracy grades.The prediction results can provide references for the selection of gear design parameters and the optimization of transmission performance in the design stage of gear systems.

INVESTIGATION OF RATTLING THRESHOLD IN GEAR SYSTEM

A lumped mass gear-rattling model with backlash is established by considering the time varying mesh stiffness, composite transmission error and the torque fluctuation. Based on the principle that no separation will occur if the response amplitude is not larger than the static response, the threshold is obtained by theoretical derivation. The validity of the theoretical derivation is verified by the numerical method. The results show that the time-varying mesh stiffness has little effect on the threshold. When the exciting frequency is less than the system natural frequency, the theoretical agrees well with the numerical one. The higher the exciting frequency or the smaller the average input torque is, the easier the separation will occur. When the exciting frequency is larger than the natural frequency by a certain value, the theoretical threshold does not agree with the numerical results. The numerical results show that the motion state will change from the meshing state to the separating state directly. The phenomenon that the gear pair sometimes separates and sometimes meshes occurs only when the exciting frequency is smaller.

Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances

A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.

Effect of integral squeeze film damper on vibration and noise of spur gear with center-distance error

When the actual installation center distance between a pair of spur gears is greater than the theoretical center distance,backlash increases,leading to increased vibration and noise.The structural parameters of an integral squeeze film damper(ISFD)were designed with the stiffness of rigid support as reference to investigate the effect of an ISFD on the dynamic characteristics of a spur gear transmission system with center-distance installation error.A spur gear test bench with center distance-error was built to investigate the vibration and noise reduction characteristics of ISFD.The experimental results indicate that,compared with a rigid support,the ISFD can reduce vibration by approximately 40%and noise by approximately 5 d B.ISFD can effectively absorb the impact energy caused by an increase of in backlash,which is conducive to the stable operation of the spur gear transmission system.

Nonlinear Dynamic Analysis of Coupled Gear-Rotor-Bearing System with the Effect of Internal and External Excitations

Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.

A Simplified Formulation to Estimate Influence of Gearbox Parameters on the Rattle Noise

Occurrence of gear rattle in transmission systems can result in severe vibration and noise,which in applications such as automobiles is an important source of user discomfort.As a result,the reduction of the rattling noise has attracted lot of concerns.The rattling noise level is affected by several gearbox parameters,an understanding of which is essential to prevent the expensive design modifications at later stages of product development.To develop such understanding at the gearbox design stage,this paper analytically evaluates the gear parameters’effect on the root mean square of the wheel gear acceleration under idling condition,which is known to be linearly correlated to the rattling noise level.Therefore,this evaluation allows for an investigation of the gear parameters’influence on the rattling noise as well.This method is then verified by comparing the analytical results with the simulation results from a dynamic model built in SIMPACK as well as previously published experimental results.Thus,the proposed analytical evaluation method can optimize the gearbox specifications at the design stage to reduce the gear rattle noise level.

Effect of nonlinear impact damping with non-integer compliance exponent on gear dynamic characteristics

A nonlinear impact damping model of single-degree-of-freedom spur cylindrical gear with backlash and time-varying stiffness was established. Systematic analyses of the dynamic responses were performed. First, the nonlinear damping coefficient was considered as a constant parameter with two types of compliance exponent, meanwhile, dynamic factors were adopted to depict the dynamic characteristics. Second, the bifurcation graphs were plotted, where the damping coefficient was obtained along with the impact velocity and coefficient of restitution. The results show that light and heavy load conditions have an effect on the responses when the compliance exponent is integer. On the contrary, when the compliance exponent is non-integer, the dynamic responses are slightly affected, namely the system is more stable than the former situation.

双曲型法向圆弧齿轮传动的动力学分析

为探究啮合刚度、传动误差及侧隙对双曲型法向圆弧齿轮传动动态响应的影响,建立齿轮副的动力学方程,并在数值计算的基础上进行仿真分析。运用有限元方法,计算接触位置处的载荷及变形,并对时变啮合刚度、静态传动误差和侧隙进行量化分析。仿真结果表明:对振动位移响应影响最大的是侧隙,其次是时变啮合刚度;对动态啮合力影响最大的则是时变啮合刚度和侧隙。

全齿轮耦合机器人齿侧间隙建模与公差仿真

鉴于全齿轮耦合机器人齿轮传动链长、反转频率高的特点,分析机器人的结构和传动原理.为了减小侧隙对机器人传动精度的影响,提出齿侧间隙理论建模及三维公差仿真分析方法.针对驱动端的圆柱齿轮机构,对齿侧间隙进行理论建模和公差仿真分析,两者相吻合.针对关节处的圆锥齿轮机构,提出将圆锥齿轮副等效为假想圆柱齿轮副的侧隙建模方法,与公差仿真分析结果吻合.以机器人肩关节偏摆传动链为分析对象计算机器人末端误差,为了降低齿侧间隙及其导致的传动链回程误差,提出圆锥齿轮加垫的计算方法和电机转角补偿方法,通过实验验证该补偿方法的有效性.

外啮合液压齿轮马达输出特性的统一简约式

为正确认识任意侧隙大小/偏置卸荷槽不同类型下齿轮马达的输出特性,基于啮合齿廓/输出特性不同的啮合线区间,以衡量侧隙大小的类型值和双卸荷槽对称线与齿轮副中心线的偏置值为变量,构建出转速/转矩等输出特性的统一简约式。结果表明,输出转速/转矩曲线可以由啮合齿廓的啮合转速/转矩曲线,通过输出特性啮合线区间的截取而直接得到;对称卸荷槽类型下的均值转速最小,均值转矩最大,转速/转矩的脉动系数最小;小侧隙较大的卸荷槽偏置范围和调速/调矩范围更大;小侧隙和对称卸荷槽类型的均值转速更小,均值转矩更大,转速/转矩的脉动系数更小;马达转矩脉动式与齿轮泵流量脉动式完全一致;转矩脉动系数略小于转速脉动系数,大齿数情况下可近似为相等;追求高转速时,应选用大侧隙和卸荷槽极限偏置的类型组合;追求大转矩或高输出脉动质量时,应选用小侧隙和对称卸荷槽的类型组合等。得出的输出特性的获取方法更简单、原理更清晰、形式更简洁、结果更可靠。

不同侧隙卸荷槽时齿轮泵理论流量的创新计算

为克服齿轮泵理论流量、排量及脉动系数计算方法的局限性与复杂性,从一个完整啮合齿面所产生的理论齿面流量入手,提出双卸荷槽间距内的理论齿面流量即为泵理论输出流量的新方法。以1.0和0.5代表侧隙的有和无,双卸荷槽对称线相对于齿轮副中心线的无量纲不对称宽度为变量,构建出理论输出流量特性的相关简洁式。结果表明:同等侧隙类型下无卸荷槽与单侧卸荷槽下的理论排量相同,有侧隙、单侧卸荷槽下的类型系数经典式确实有误;无侧隙、对称卸荷槽类型下的理论排量更大,流量脉动更小,但困油现象更严重;尤其单侧卸荷槽下的流量脉动很大和困油现象很严重,不建议采用等。本文提出的新方法原理更清晰,公式更简洁,结果更可靠,通用性更强。

机器人用同轴磁性齿轮若干基本特性分析及其数值计算

机器人用同轴磁性齿轮受其固有特性的限制,目前难以直接应用于工业机器人,其力矩密度、传动比、空程、背隙和扭转刚度、稳定工作区等关键基本特性的研究尚存不足。为此,以国家标准规定的型14谐波齿轮性能为参考对象,采用类比的方法,运用相关电磁学理论,对与其同等空间大小的同轴磁性齿轮相关性能及其数值计算方法、稳定性以及伺服电动机和同轴磁性齿轮的一体化集成技术进行了研究和对比,指出了扭转刚度不足是制约同轴磁性齿轮用于机器人的关键因素,明确了未来机器人同轴磁性齿轮伺服控制的研究重点。

热变形不同工况参数对行星齿轮系统齿隙影响规律研究

针对不同工况条件下,行星齿轮系统的齿侧间隙因热变形所发生的改变,提出一种包含内啮合副热变形的行星齿轮系统齿侧间隙改变量理论计算模型。利用ANSYS Workbench稳态热-结构耦合场对所提出的模型进行验证,获得不同工况下的稳态温度场数据。基于所提出的模型并结合稳态温度场数据,分析变转速、变扭矩以及恒功率3种工况下,行星齿轮系统齿侧间隙随工况参数的变化规律,可为行星齿轮系统的动力学分析提供理论依据。

全数控螺旋锥齿轮铣齿机双电机消隙技术研究

作为加工螺旋锥齿轮的专用设备,螺旋锥齿轮铣齿机在数控加工过程中由于齿隙的存在易出现卡死问题,引致冲击与震荡等现象,降低齿轮加工精度。对比消隙技术,构建基于PMAC的螺旋锥齿轮铣齿机传动系统双电机消隙方法,应用IPC+PMAC运动控制器的双电机驱动应用系统对该消隙方法进行试验,结果表明此方法能有效消除齿隙,提升整个数控系统的稳定性,利用双电机伺服消隙方法具有一定的可靠性。

电动舵机内部扰动分析及建模

电动舵机中的减速机构通常会引入齿隙和摩擦等非线性内部扰动,此类非线性扰动会对电动舵机的动、静态性能造成一定影响。针对电动舵机减速器造成的内部扰动进行了分析,为了解除两级减速器内部的耦合关系,将其分为2个部分分别进行建模,再进行串联仿真。基于蜗轮蜗杆减速器建立了随外部负载变化的非线性摩擦模型,基于圆柱齿轮减速器建立了包含非线性力矩传递特性的齿隙模型。通过将模型仿真结果与舵机实测结果进行对比,确认了模型与舵机具有相同的非线性特性,验证了电动舵机内部扰动的来源,并为舵机控制算法的研究提供了良好的平台。